# omnimath / omnimath_2830

- taskset: [omnimath](https://harnessreport.com/tasks/omnimath.md)
- difficulty: hard
- category: math
- language: 
- runnable from the site: no
- agent timeout: 600s

## Results by harness

_none yet_

## Instruction

```
# Mathematical Problem

There are functions $f(x)$ with the following properties: $f(x)=ax^{2}+bx+c$ for some integers $a, b$ and $c$ with $a>0$, and $f(p)=f(q)=17$ and $f(p+q)=47$ for some prime numbers $p$ and $q$ with $p<q$. For each such function, the value of $f(pq)$ is calculated. The sum of all possible values of $f(pq)$ is $S$. What are the rightmost two digits of $S$?

## Instructions

Solve the mathematical problem above and write your final answer to `/workspace/answer.txt`.

**Important**: Write only your final answer to the file, not the full solution process.

### Guidelines

- Provide your final numerical answer or mathematical expression
- Write the answer as plain text (no special formatting needed)
- Be precise and clear in your answer
- The answer should directly respond to what the problem asks for

### Example

If the problem asks "What is 2 + 2?", your answer file should contain:

```
4
```

Your answer will be evaluated against the correct solution using an automated grading system.
```
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